Its not as simple as that. Each ring individually would produce a diffraction pattern with a wave amplitude that is a J_0 Bessel function, with a peak on the axis and lower elsewhere. At any point in the image plane the J_0 contributions from all the rings combine with random phases, but just as...
I have been considering the properties of a Diffractive Optical Element (DOE) consisting of a very large number of concentric rings of equal (small) width, where the thicknessses of the rings are such as to produce random phase shifts in the range 0 to 2pi. I think I understand the behaviour of...
Much of this discussion is correct but not very revealing. The key thing to remember is that the work done by a force is the product of that force and the movement of its point of application IN THE DIRECTION OF THAT FORCE. Using cartesian coordinates with origin at the initial position the...
1) I agree with the various comments about systematic errors
2) I am a bit worried about the statement "CPM is being measured" If "CPM" is Counts per minute then you can't use
Error= SQRT(value)
unless the measure is over exactly 1 minute. Fir thius tio be valid "value" must be a count...
I think Gleem's formula is correct, but its messy to expand. Its easier to consider the inverse ratio D = 1/CR = (W+R)/W = 1+(R/W) and then use s(CR)/R = s(D)/D.
Care is needed here in several respects
1) For Poisson Statsistics to be used it is indeed important that W and R are not rates, but counts in the same interval of time. In that case the standard errors on W and on R+W are indeed Sqrt(R) and Sqrt(R+W) ie the sqrt of the counts in each case
You...
You are considering looking at the fringe pattern as a way of measuring wavelength, which is fine because the fringe pitch is proportional to wavelength. If you see only a few fringes then you have only an approximate measure of wavelength.
This is getting to the crux of it.
If you believe...
Consider a Double Slits experiment in which the light source is monochromatic and each slit very narrow. There will be many fringes visible on either side of the axis.
1) If the light source is pulsed with very short, randomly spaced, pulses it will produce spectrally broadened radiation and...
It doesn't have to be femtosecond, just sufficiently short that the spectrum is broadened. And it doesn't have to be a mechanical shutter.
The real question is whether the focussing of a chromatic optical system can be affected by the brevity or otherwise of the intervals (frames) during which...
A recent preprint ( https://arxiv.org/abs/2112.15157 ) seems to imply that the focussing properties of an optical system can depend on the bandwidth of the sensor, and even on that of the associated electronics! It is argued there that if the ‘frame rate’ of the sensor is very high, photons...